Work
__TOC__ Definition Thermodynamically, work is defined as a process in which energy is transferred across a system boundary. Work can be thought of as an effect of one system imposed onto another (e.g. a thermodynamic system acting on its surroundings). The presence of work done by a system is measured by the following statement, "Work is done by a system on its surroundings if the sole effect of everything external to the system could have been produced by the raising of a weight" [2]. It should be noted that from this statement it is not necessary for a system to physically raise a weight (or essentially have a force act across a distance) to have work been performed, but rather that the same effect on the system ''could have ''been replicated by raising a weight. Joule's Experiments To further understand this process of energy transfer, it is worth examining a series of experiments performed by James Prescott Joule in the 1840's. In his experiments, he aimed to determine the mechanical energy (i.e. mechanical work) necessary to raise the temperature inside a water bath by 1 °F. For these experiments, there was bath of water which would be set up to be effected by various sources of work. First Experiment The first set-up consisted of a propeller and weight apparatus to supply work to the water bath. Essentially, the work necessary to raise the temperature of the water bath for this experiment was able to be quantified by measuring the vertical displace (dy) of the mass. It was determined that 773 ft*lbf was required to raise the temperature in the water bath by 1 °F. Second Experiment The second experiment consisted of two masses, one directly on top of another. Also, an outward force was applied to the top mass (creating heating of the water bath due to friction). Overall, the work necessary to raise the temperature of the water bath for this experiment was quantified by measuring the horizontal force across the displacement (dx). It was determined that 775 ft*lbf was required to raise the temperature in the water bath by 1 °F. Third Experiment The third experiment consisted of a piston cylinder sytem located inside the water bath. From this set-up, a force is applied to the piston to essentially compress the cylinder (creating heating of the water bath due to compressive work). Essentially, the work necessary to raise the temperature of the water bath for this experiment was determined by quantifying the force applied to the cylinder over the displacement (dx). It was determined that 793 ft*lbf was required to raise the temperature in the water bath by 1 °F. From these experiments, it is apparent that by applying various types work to a system, it is possible to generate heat within the system. Essentially, due to all three of the systems being insulated, there is no heat transferred from the systems to the surroundings. Then, from the First Law of Thermodynamics (Energy Conservation), with the work applied to the system, the internal energy of the water bath must increase. Also, it should be noted that the work required to raise the bath temperature 1 °F for each of the various external work sources is essentially constants across the various experiments. Due to the constant volume nature of the systems in Joule's Experiments, the amount of work applied to the system necessary to raise the water bath 1 °F is now realized as the specific heat at constant volume for water (which Joule measured to be approximately 781 (ft*lbf)/(lbm*R) and is now accepted to be 778 (ft*lbf)/(lbm*R)). Simple Compressible Substance When considering thermodynamics, it is often useful to apply the simple compressible substance assumption to a flow system. Under this assumption, the only type of work that can naturally occur on the flow system is fluid compression work. "This term designates substances whose surface effects, magnetic effects, and electrical effects are insignificant when dealing with compressible substances" [1]. Fluid compression work, or "pdV" work as it is sometimes called, is a type of reversible work which is quantified by the following equation: W = pdV , where p is the pressure of the fluid & dV is a finite change in volume of the fluid. From this relation, it is apparent that when a fluid is expanded (positive dV value), work is released from the system, and while the fluid is compressed (negative dV value), work must be supplied to the system. Thus, this relation will adequately describe the compression and expansion of a simple compressible fluid. Once applying this assumption to the First Law of Thermodynamics, many thermodynamic systems (often of which are applicable to the field of aerospace engineering) can be simplfied and solved. Reversible / Irreversible / Impossible Processes While discussing the concept of work in thermodynamics, it is important to consider the type of processes a system can undergo. Thermodynamic processes can be divided into the three following designation: Reversible, Irreversible and Impossible. Differentiating between the three is directly attributed to the Second Law of Thermodynamics and the production of entropy. Reversible Process Essentially, a reversible process is an ideal thermodynamic process. In other words, when a process is reversible, no change on a system or its surroundings has taken place 1. Thus, the process that initially took place is able to be reversed with no net change in the entropy of the system present (i,e. Entropy Production, Ps = 0). Due to the entropy staying constant, reversible processes are the most efficient as apposed to processes with entropy generation. One type of reversible process would be an extremely slow process (e.g. upon considering combustion, an example would be an ideal gas mixture having enough time to reach equilibrium) 3. Reversible Process: \Delta s = Ps = 0 Irreversible Process An irreversible process Irreversible Process: Ps \ge 0 Impossible Process: Ps < 0 References 1 Sonntag, Richard E., Claus Borgnakke and Gordon J. Van Wylen. Fundamentals of Thermodynamics: Sixth Edition. John Wiley & Sons, Inc., 2003. 2 Bejan, Adrian, George Tsatsaronis and Michael Moran. Thermal Design & Optimization. John Wiley & Sons, Inc., 1996. 3 Denbigh, Kenneth. The Principles of Chemical Equilibrium: Fourth Edition. Cambridge University Press, 1997.